Nonreciprocal light propagation effects are of great interest
in order to design devices such as isolators and circulators that can
prevent undesired backward reflection and interference effects in optical circuits.
A typical way to attain such effects relies on magneto-optical
materials which, in the presence of a (static) bias magnetic field that breaks
the time-reversal symmetry, are characterized by different propagation constants for
circularly polarized waves with right- and left-handedness.
However, the magneto-optical activity of candidate materials, such as bismuth iron garnet,
is quite weak at optical frequencies, thereby leading to rather bulky implementations.
Therefore, several strategies have been explored in order to achieve significant response enhancements,
all essentially based on the coupling of magneto-electric effects with resonant phenomena.

In some recent investigations, in collaboration with Nader Engheta (University of Pennsylvania) and
Andrea Alù (University of Texas at Austin), we have explored the
unidirectional resonant photon tunneling through heterostructures containing magneto-optical constituents.
Our ideas essentially rely on the large body of results available on
resonant photon tunneling phenomena in multilayered heterostructures
combining single-negative (i.e., with negative permittivity or permeability) and double-positive
(i.e., with positive permittivity and permeability) material constituents.
By inserting in these heterostructures magneto-optical materials,
we render the resonance conditions sensitive to the circular polarization handedness.

More specifically, in [1], we studied the resonant tunnelling effects that can occur in
trilayer structures featuring a
dielectric layer sandwiched between two magneto-optical-metal (e.g., \(Co_6Ag_{94}\)) layers.
We showed that the resonance splitting associated with these phenomena can be exploited to enhance
Faraday rotation at optical frequencies. Our results indicate that, in the presence of realistic loss levels,
a tri-layer structure of subwavelength thickness is capable of yielding sensible (∼10◦)
Faraday rotation with transmittance levels that are an order of magnitude larger than those
attainable with a standalone slab of magneto-optical-metal metal of the same thickness.

In [2],
we showed that tri-layer structures combining epsilon-negative and
magneto-optical material layers can exhibit unidirectional resonant photon
tunneling phenomena that can discriminate between circularly polarized waves of
given handedness impinging from opposite directions, or between circularly polarized waves with different handedness
impinging from the same direction.
The figure top panel illustrates the configuration considered, consisting of a magneto-electric layer sandwiched
between two epsilon-negative layers.
The bottom panel shows the resonant field distributions of electric (solid) and magnetic (dashed) fields
for right-handed circularly polarized plane-wave illumination
impinging from left and right. For incidence from left,
total transmission is clearly visible, with evanescent field growth in the left epsilon-negative layer,
and the electric and magnetic fields peaked at the center of the magneto-optical layer and at its boundaries
with the epsilon-negative layers,
respectively. The response resembles that of a Fabry-Perot resonant cavity, effectively
formed by the highly reflective properties of the epsilon-negative end layers. Conversely, for incidence from right,
a strong reflection and very low transmission are observed.
Our results indicate that this phenomenon is satisfactorily robust with respect to unavoidable nonidealities,
and can be exploited to design compact (wavelength-sized) optical isolators for circularly polarized waves.

We study resonant tunnelling effects that can occur in trilayer structures featuring a dielectric layer sandwiched between two magneto-optical(MO)-metal layers. We show that the resonance splitting associated with these phenomena can be exploited to enhance Faraday rotation at optical frequencies. Our results indicate that, in the presence of realistic loss levels, a tri-layer structure of subwavelength thickness is capable of yielding sensible (\(∼10^o\)) Faraday rotation with transmittance levels that are an order of magnitude larger than those attainable with a standalone slab of MO metal of the same thickness.

We show that tri-layer structures combining epsilon-negative and magneto-optical material layers can exhibit unidirectional resonant photon tunneling phenomena that can discriminate between circularly polarized (CP) waves of given handedness impinging from opposite directions, or between CP waves with different handedness impinging from the same direction. This physical principle, which can also be interpreted in terms of a Fabry-Perot-type resonance, may be utilized to design compact optical isolators for CP waves. Within this framework, we derive simple analytical conditions and design formulae, and quantitatively assess the isolation performance, also taking into account the unavoidable imperfections and nonidealities.